<h2>Problem 146</h2>
<div style="color:#666;font-size:80%;">24 March 2007</div><br />
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<p>The smallest positive integer <i>n</i> for which the numbers <i>n</i><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />+1, <i>n</i><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />+3, <i>n</i><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />+7, <i>n</i><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />+9, <i>n</i><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />+13, and <i>n</i><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />+27 are consecutive primes is 10. The sum of all such integers <i>n</i> below one-million is 1242490.</p>

<p>What is the sum of all such integers <i>n</i> below 150 million?</p>
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